Unsupervised Feature Selection via Nonnegative Spectral Analysis and Redundancy Control

In many image processing and pattern recognition problems, visual contents of images are currently described by high-dimensional features, which are often redundant and noisy. Toward this end, we propose a novel unsupervised feature selection scheme, namely, nonnegative spectral analysis with constrained redundancy, by jointly leveraging nonnegative spectral clustering and redundancy analysis. The proposed method can directly identify a discriminative subset of the most useful and redundancy-constrained features. Nonnegative spectral analysis is developed to learn more accurate cluster labels of the input images, during which the feature selection is performed simultaneously. The joint learning of the cluster labels and feature selection matrix enables to select the most discriminative features. Row-wise sparse models with a general ℓ(2, p)-norm (0 < p ≤ 1) are leveraged to make the proposed model suitable for feature selection and robust to noise. Besides, the redundancy between features is explicitly exploited to control the redundancy of the selected subset. The proposed problem is formulated as an optimization problem with a well-defined objective function solved by the developed simple yet efficient iterative algorithm. Finally, we conduct extensive experiments on nine diverse image benchmarks, including face data, handwritten digit data, and object image data. The proposed method achieves encouraging the experimental results in comparison with several representative algorithms, which demonstrates the effectiveness of the proposed algorithm for unsupervised feature selection.